Let's solve for x first.
To find x, use the interior angles on same side of a transversal theorem.
The interior angles on sam side of a transversal are supplemantary angles, and supplementary angles sum up to 180 degrees.
Thus, we have:
(23x - 16) + (8x - 21) = 180
23x - 16 + 8x - 21 = 180
Combine like terms:
23x + 8x - 21 - 16 = 180
31x - 37 = 180
Add 37 to both sides:
31x - 37 + 37 = 180 + 37
31x = 217
Divide both sides by 31:
[tex]\begin{gathered} \frac{31x}{31}=\frac{217}{31} \\ \\ x\text{ = 7} \end{gathered}[/tex]
To find y, use the vertical angles theorem.
Vertical angles are congruent.
Thus we have:
7y - 23 = 23x - 16
Since x = 7, substitute x for 7 in the equation above to find y.
7y - 23 = 23(7) - 16
7y - 23 = 161 - 16
7y - 23 = 145
Add 23 to both sides:
7y - 23 + 23 = 145 + 23
7y = 168
Divide both sides by 7:
[tex]\begin{gathered} \frac{7y}{7}=\frac{168}{7} \\ \\ y\text{ = }24 \end{gathered}[/tex]
x = 7
y = 24
ANSWER:
x = 7
y = 24
